Answer:
One-third(7)(12)(10) – One-thirdπ(3^2)(10)
280 – 30π
Step-by-step explanation:
step 1
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=6/2=3\ units[/tex] ---> the radius is half the diameter
[tex]h=10\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (3)^{2}(10)[/tex]
[tex]V=30\pi\ units^3[/tex]
step 2
Find the volume of the rectangular pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
[tex]B=(7)(12)=84\ units^2[/tex]
[tex]h=10\ units[/tex]
substitute
[tex]V=\frac{1}{3}(84)(10)[/tex]
[tex]V=280\ units^3[/tex]
step 3
Find the volume of the composite figure
we know that
The volume of the composite figure is equal to subtract the volume of the cone from the volume of the rectangular pyramid
so
[tex]V=(280-30\pi)\ units^3[/tex]
